Context
I'll be using a Nikon 300mm/f4 on my Sony a6000 and seeing what birds I can get with it. The Sony 55-210mm is what I've been using but it lacks the reach and native teleconverters.
Autofocusing on the Sony with that lens works but a good chunk of the time it focuses on the closest item, which may be a branch which doesn't help so I have to manually focus on the bird.
Question
I know that the fancy new Nikon 300mm/f2.8 and 400mm/f2.8 lens have fast autofocusing speed, some people say it's faster than a 70-200/f2.8. Do pros still rely on autofocusing for birds and other animals where they may be partially visible (e.g. behind a bush) or do they manually focus to get it just right?
I'm asking this as my Sony seems to focus too much to the front and misses the bird usually behind a branch or related so I'm focused to manually focus. I presume Pro DSLR bodies don't have this problem?